I think that some more info would help. What kind of money do you have to spend? Do you intend to play with other musicians soon? If so, what type of songs?
Anyway, give us some background, and I'm sure you'll get plenty of advice.

I'm guessing, that a combo would be best. It's self contained, and easier to lug around. Probably more affordable, too. There are some really nice ones out there.

As you get better, and more serious, you could consider upgrading to a more pro, more expensive rig.
Go to a big store, with your bass, and plug into some things. See what sounds best to you. If you like something, check E-bay, for a deal.

Also do you plan on playing bass for a while? Or just kinda testing it out? Because if you are gonna play for awhile it'd make more sense to start off with a decent amp so you can save some money in the long run.

You have lots of choices. The following will work well with Fenders. they are warm b/c that is what I like. the other end of the spectrum is hartke, peavey and GK. But if you have a Precision or Jazz Bass, then I am assuming some thing about the tone you are after.

Ampeg B100R

Ashdown Mag 210

Nemises 115 or 210

Yorkville 115 or 210 they have a 200 watt and 400 watt. The 400 watt is a little over budget, about 600 at an aggressive dealer.

when they say 115, the mean 1 15" speaker
210 means two 10" speakers.

The more watts the better.

The tone is subjective. they all sound completely different. some are aggressive (harsh) some are smooth some are warm with a little bite. this is where things get tough. but the ones i mentioned are all player amps, not really beginner ones. you have a good budget to work with. these are amps you could easily sell if you didn't like. But they are good enough to where they won't limit your ability to sound good, like many practice combos.

angelopb's list is a really good start. Those are some phat sounding amps. Also check out SWR. You should take your bass to the music store and play thru as many different amps in your price range as you can. Don't overlook used amps either. With $500 to spend, with some smart shopping you may land yourself a much better amp than you would buying new.
One more bit of advice....if you have a friend who is an experienced bass player, get him/her to go with you. That can be most helpful in sorting thru different features on different amps, and also help cut thru a lot of salesman B.S.